方程2x2-xy-3x+y+2006=0的正整数解(x,y)共有_对.
题目
方程2x2-xy-3x+y+2006=0的正整数解(x,y)共有______对.
答案
2x2-xy-3x+y+2006=0,∴-2x2+xy+2x+x-y=2006∴(2x-2x2)+(xy-y)+(x-1)=2006-1,∴-2x(x-1)+y(x-1)+(x-1)=2005,∴(x-1)(y+1-2x)=2005=5×401当①x-1=1,y+1-2x=2005,即(x,y)=(2,2008)当②x-1=...
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